Reinhold Schneider: Wavelet Subspace Splitting
Wavelet bases offer a modern tool for an efficient approximation of
functions and operators. However in many situations wavelet bases
are not appropriate or are far to be optimal bases for an actual
We show how to construct basis
functions which are more adapted to this situations
by taking linear combinations of wavelet bases, e.g.
wavelet packets or wavelet clusters.
With these techniques at hand, it is possible to built appropriate
basis functions e.g. to approximate
singularities of Kato type or to achieve an exponential convergence rate for
the approximation of analytic functions.